Simplify; express your answer in exponential form. Assume $x\neq 0, k\neq 0$. $\dfrac{{x}}{{(x^{5}k^{3})^{2}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${x}$ to the exponent ${1}$ . Now ${1 \times 1 = 1}$ , so ${x = x}$ In the denominator, we can use the distributive property of exponents. ${(x^{5}k^{3})^{2} = (x^{5})^{2}(k^{3})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{x}}{{(x^{5}k^{3})^{2}}} = \dfrac{{x}}{{x^{10}k^{6}}}$ Break up the equation by variable and simplify. $\dfrac{{x}}{{x^{10}k^{6}}} = \dfrac{{x}}{{x^{10}}} \cdot \dfrac{{1}}{{k^{6}}} = x^{{1} - {10}} \cdot k^{- {6}} = x^{-9}k^{-6}$.